A lattice Boltzmann method is developed for gaseous slip flow at the pore scale in microscale porous geometries. Flow characteristics through various porous structures are studied for different Knudsen numbers and inlet to outlet pressure ratios. It is found that the gas permeability is larger than the absolute permeability of porous media due to the gas slippage effect. Furthermore, the rarefaction influence on the gas permeability is more evident for porous structures with low porosity. The Klinkenberg equation is confirmed for the simulated porous structures. However, the second-order term of the Knudsen number $\left({\mathrm{Kn}}^2\right)$ cannot be neglected for gaseous flow with relatively high Knudsen numbers. A model for predicting the pressure drop of the flow through microscale porous media is presented based on the Ergun equation and the Carman-Kozeny equation by taking into account the effects of gas rarefaction and compressibility.

A thermal boundary condition for a double-population thermal lattice Boltzmann equation (TLBE) is introduced and numerically demonstrated. The unknown distribution population at the boundary node is decomposed into its equilibrium part and nonequilibrium parts, and then the nonequilibrium part is approximated with a first-order extrapolation of the nonequilibrium part of the populations at the neighboring fluid nodes. Numerical tests with Dirichlet and Neumann boundary constraints show that the numerical results of the TLBE together with the present boundary schemes agree well with the analytical solutions and those of the finite-volume method.